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Averaging principle for equation driven by a stochastic measure

Vadym Radchenko

Abstract

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only $σ$-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for this case, the rate of convergence to the solution of the averaged equation is estimated.

Averaging principle for equation driven by a stochastic measure

Abstract

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only -additivity in probability and continuity of the paths. It is proved that the averaging principle holds for this case, the rate of convergence to the solution of the averaged equation is estimated.

Paper Structure

This paper contains 5 sections, 5 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Stochastic measures
  4. Symmetric integral
  5. Averaging principle

Key Result

Lemma 2.2

(Corollary 3.3 rads16) If Aassintm holds then the set of random variables is bounded in probability.

Theorems & Definitions (10)

  • Definition 2.1
  • Lemma 2.2
  • Definition 2.3
  • Theorem 2.4
  • Definition 2.5
  • Theorem 2.6
  • Theorem 3.1
  • proof
  • Corollary 3.2
  • Remark 1